Neural networks have shown tremendous potential for reconstructing high-resolution images in inverse problems. The non-convex and opaque nature of neural networks, however, hinders their utility in sensitive applications such as medical imaging. To cope with this challenge, this paper advocates a convex duality framework that makes a two-layer fully-convolutional ReLU denoising network amenable to convex optimization. The convex dual network not only offers the optimum training with convex solvers, but also facilitates interpreting training and prediction. In particular, it implies training neural networks with weight decay regularization induces path sparsity while the prediction is piecewise linear filtering. A range of experiments with MNIST and fastMRI datasets confirm the efficacy of the dual network optimization problem.

本文提出了一种凸二元框架用于优化神经网络，从而解决了其在敏感应用如医学成像中的非凸和不透明性质的问题。该凸对偶网络不仅能够通过凸优化器获得最优训练，还有利于训练和预测的解释，特别是通过权重衰减正则化训练神经网络，诱导路径稀疏性的同时，预测是分段线性滤波。实验结果表明，该凸对偶网络优化问题在MNIST和fastMRI数据集上有效。

神经重建背后的凸正则化